About two decades ago, a prominent New York lawyer named Ernest Patrikis met in China with Zhu Rongji, who at the time was the nation's second-highest-ranking government official and who later would become premier. When Mr. Patrikis, the general counsel at the Federal Reserve Bank of New York, prepared to leave along with the New York Fed president, Mr. Zhu stopped both men and told them: "Give my regards to Hank Greenberg."

That long-distance salutation came in the middle of Maurice "Hank" Greenberg's 38-year-long reign at American International Group, which ended abruptly in 2005. What's striking is that Mr. Greenberg still wields the same sort of clout years after his defenestration and his company's subsequent collapse into the mother of all bailouts.

Despite all that, Mr. Greenberg ranks No. 1 on Crain's list of the most-connected New Yorkers. The list, powered by Manhattan-based Relationship Science, used proprietary algorithms that captured the relationships of nearly 16,000 leaders tied to more than 1,000 of the New York area's top corporate, financial and nonprofit institutions.

Mr. Greenberg, 89, emerges as No. 1 because during his lifetime he has amassed impressive totals of both direct connections and strong connections to thousands of other highly connected individuals and organizations. Mr. Greenberg is so connected, there's a good chance he is the fastest link between two unconnected people in that universe of 16,000 New York executives.

When told of his accomplishment, Mr. Greenberg sniffed: "Not surprising."Really, he was asked, not at all surprised?

"Well," he said, yielding just a bit. "I guess what is a little surprising is I rank that high even though I'm not running AIG."

Longevity's rewards

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Indeed, Mr. Greenberg is now master of a much smaller domain. He is chairman and CEO of an insurer called Starr Cos., which has 3,000 employees, or 2.5% of what AIG had at its peak. Starr's U.S. arm wrote $1.3 billion worth of gross premiums last year to insure such things as airplanes, copper mines and vacation properties, according to research firm A.M. Best. AIG last year wrote $45 billion in gross property and casualty premiums.

So it's fair to say it isn't Mr. Greenberg's current job that makes him the city's most connected business executive. Instead, it reflects Mr. Greenberg's extraordinary longevity and success in the corporate insurance industry, where he started in 1952. Building AIG into a company that had a market value of $242 billion at its height, in 2000, enabled him to fund the massive Starr Foundation, which donates tens of millions annually to nonprofits. That, in turn, has opened the door to seats on dozens of nonprofit boards, which in turn buttress his business connections.

Prominent city institutions whose walls are embossed with the names of Mr. Greenberg and his mentor, AIG founder Cornelius Vander Starr, include the Greenberg Center for Geoeconomic Studies at the Council on Foreign Relations, the Greenberg Pavilion at the Weill Cornell Medical Center, the C.V. Starr East Asian Library at Columbia University, the C.V. Starr Virtual Herbarium at the New York Botanical Garden and the Starr Fund for Collaborative Science at Rockefeller University.

Scholarship funds named for Mr. Greenberg and Vander Starr can be found at Baruch College, Columbia, the Juilliard School, New York Law School and the School of American Ballet, among others.

Last year, the Starr Foundation gave $25 million to the Hebrew Home at Riverdale because, Mr. Greenberg said, his mother lived there until she died at 94. The mother of a friend, former Citigroup CEO Sandy Weill, also resided there, and Mr. Greenberg recalled that the home sent people to check on the mother of a former AIG advisory board member—Henry Kissinger—so that she could remain in her apartment.

Yet the Starr Foundation isn't what it used to be. Ten years ago, it held $3.5 billion in assets, nearly all of it AIG stock, and made about $170 million in grants in 2004. But about $2 billion vaporized when AIG collapsed in 2008, and by 2012 the foundation controlled just $1.3 billion in assets and made about $75 million in grants. (An IRS filing shows the foundation now has less than $6 million invested in AIG.)

Even in its shrunken form, Starr is still the 13th-largest foundation in the city, and Mr. Greenberg's ties to New York's business and philanthropic elite remain second to none.

Consider the night of June 5, when he served as vice chairman of the Japan Society's annual dinner, which was chaired by Wilbur Ross, a private-equity executive whose funds manage $17 million for the Starr Foundation. But Mr. Greenberg said he couldn't attend the Japan event because he was going to the Plaza Hotel for a gala hosted by New York-Presbyterian Hospital, which was honoring a doctor with the 34th annual Maurice R. Greenberg Distinguished Service Award.

Mr. Greenberg's long involvement with the hospital has given him insights that help his insurance business. For instance, earlier this year his company acquired a medical claims processor called Multi-Plan for a reported $4.4 billion.

Still fighting AIG lawsuits

His connections might even help him finance his lawsuit against the U.S. government, which he alleges illegally seized AIG during the 2008 bailout. Wall Street titans Steven Cohen, Kenneth Langone and J. Christopher Flowers reportedly may help pay Mr. Greenberg's legal team, led by David Boies, in exchange for a piece of the proceeds should Mr. Greenberg win some of the $55.5 billion in damages he's seeking. The Starr Foundation has invested about $25 million in Mr. Flowers' private-equity funds.

That's not his only legal war. A New York state judge in May ordered a trial over a lawsuit filed nine years ago by then Attorney General Eliot Spitzer. The suit alleges that Mr. Greenberg participated in the accounting games that led to his ouster at AIG, a charge that he adamantly denies. No date has been set for the trial, now being handled by Attorney General Eric Schneiderman.

In the meantime, Mr. Greenberg is keen to convey that he's still very much a player in finance. Starr is growing fast, with its U.S. subsidiary generating $20.6 million in pretax income last year, according to A.M. Best, up from $1.9 million in 2010. Clients include American Express, Diamond Resorts and Freeport McMoran Copper & Gold, according to filings. Mr. Greenberg said his firm is adding to its real estate and investment management businesses.

He still visits China four or five times a year—Vander Starr founded AIG's predecessor firm in Shanghai in 1919 and moved it to New York in 1939—and he's planning an around-the-world business trip in July, though he wouldn't cite where he's going for "security reasons."

"I'm doing everything I normally do," he said. "I love building."

Editor's note: C.V. Starr & Co. Is one of the investors in Relationship Science. The firm's outside investors had no role in determining RelSci's and Crain's rankings of the Most-Connected New Yorkers.